Method and tool for securing a bearing race within a bore in a housing

ABSTRACT

An annular shoulder which retains a bearing race in a bore in a housing is swaged by beveled rollers mounted on a rotatable spindle. Pressure exerted by the rollers against the shoulder is maintained at a first predetermined level during at least half of a revolution of the spindle, then is increased to a second predetermined level while the spindle continues to rotate, and finally is maintained at the second level during at least half of a revolution of the spindle. The bevel of the rollers, radius of their larger diameter edges, and distance between their inner sides are designed to provide proper swaging of the shoulder.

United States Patent Shiilet Feb. 8, 1972 [54] METHOD AND TOOL FOR SECURING A BEARING RACE WITHIN A BORE IN A HOUSING UNITED STATES PATENTS 3,444,606 5/1969 Jones ..29/149.5 B X Primary ExaminerThomas H. Eager Attorney-George E. Pearson [57] ABSTRACT An annular shoulder which retains a bearing race in a bore in a housing is swaged by beveled rollers mounted on a rotatable spindle. Pressure exerted by the rollers against the shoulder is maintained at a first predetermined level during at least half of a revolution of the spindle, then is increased to a second predetermined level while the spindle continues to rotate, and finally is maintained at the second level during at least half of a revolution of the spindle. The bevel of the rollers, radius of their larger diameter edges, and distance between their inner sides are designed to provide proper swaging of the shoulder.

8 Claims, 4 Drawing Figures Cl 2 i so /70 i l P I l l I PATENTED FEB 8 m2 SHEET 1 0r 2 INVENTOR, ROBERT H. SHIFLET llll nl FIGZ -l||l llllil F lllllll PATENTEU FEB 8 I972 SHEEI 2 [IF 2 I I I II II I II? II FIG. 4

INVENTOR. ROBERT H. SHIFLET IIIII IIILIII FIG. 3

METHOD AND TOOL FOR SECURING A BEARING RACE WITHIN A BORE IN A HOUSING BACKGROUND OF THE INVENTION In modern aircraft a large number of parts are provided with spherical bearings the races of which are fixedly positioned within bores in various structures, hereinafter referred to as hearing housings. Often such a bearing has annular grooves formed in opposite sides of its race, and to hold the bearing within the bore of its housing the edge portions of said race which lie outside said grooves are swaged over chamfers formed on the edges of said bore. Also in some cases an annular groove is formed in a bearing housing in concentric relation with the edge of the bore in which a spherical bearing is to be seated, and the edge portion of said housing which lies between said groove and the wall of said bore is swaged over a chamfered edge on the bearing race. The development of large and powerful jet-propelled aircraft has required that both spherical bearings and bearing housings in such aircraft be made of high-strength alloys, and consequently great difficulty has been encountered in attempts to swage such bearings and housings by means of known roller swaging tools. More specifically, the use of roller swaging tools of the prior art in the swaging of spherical bearings and housings which are formed of high-strength alloys causes various unacceptable installation defects, including galling and distortion in the bearing races and cracking in the retaining lips of said races or their housings.

SUMMARY OF THE INVENTION This invention relates to an improved roller swaging tool and method of its use. More particularly, by means of the tool and method disclosed herein annular shoulders on highstrength spherical hearings, or on their housings, can be deformed to thereby secure said components to one another without installation defects of the type heretofore mentioned.

In one swaging tool in accordance with the invention a pair of rollers are mounted on opposite sides of a spindle and arranged so that beveled surfaces thereof can be positioned against the outer wall of an annular, V-shaped groove formed in one side of the race of a spherical bearing, which race is adapted to fit with a bore in a bearing housing and is held therein by swaging over a chamfered edge of said bore the portion of said race which lies outside said groove. One end of the spindle is adapted to fit snugly within the inner, rotatable member of the bearing, and the spacing between the rollers of the swaging tool is set at a predetermined distance relative to the center-tocenter diameter of the aforesaid groove in the bearing race. The larger diameter edges of the beveled swaging surfaces of the rollers have a selected radius of curvature which, in conjunction with the spacing between the rollers and the angle of their beveled swaging surfaces, enables the bearing race retaining shoulder to be swaged without installation defects when the swaging tool is used in the proper manner, which requires that (l) the rollers are initially pressed against said shoulder under a first predetermined pressure while the spindle is rotated at least half of a revolution about its longitudinal axis, (2) the pressure exerted against the shoulder is then increased to a second predetermined pressure while the rollers continue to roll around said shoulder, and (3) the rollers are rolled a predetermined distance around the shoulder while the second pressure is maintained.

DESCRIPTION OF THE DRAWINGS FIG. 1 is an elevation of a first swaging tool in accordance with the invention, the drawing also illustrating in sectional form a spherical bearing and the housing therefor and in partially section form a support anvil for said bearing and housmg.

FIG. 2 is another view of the first swaging tool, bearing, and housing shown in FIG. 1, the drawing illustrating a different support anvil for the bearing and a different position of said bearing and said housing.

FIG. 3 is an elevation of a second swaging tool in accordance with the invention, the drawing also illustrating in sectional form a spherical bearing and the housing therefore and in partially sectional form a support anvil for said bearing and housing.

FIG. 4 is another view of the second swaging tool, bearing, and housing shown in FIG. 3, the drawing illustrating a different support anvil for the bearing and a different position of said bearing and said housing.

DETAILED DESCRIPTION First Embodiment In FIG. 1 reference number 10 designates generally a swaging tool having a spindle 12 one end of which is adapted to be fixedly disposed within the apertured end of a rotatable ram 14 and the other end of which is slidable within the aperture in the rotatable member (or ball) 16 of a spherical bearing 18. The race 20 of bearing 18 fits snugly within a bore 22 formed in the housing 24 for said bearing, and during a first swaging operation performed by tool 10 and described hereinafter, both said race and said housing are preferably supported upon the flat upper surface of a centrally apertured, cylindrical support anvil 26 which includes a counterbore 28 providing clearance for member 16. The end of spindle 12 which fits within the aperture in member 16 also fits snugly within a reduced diameter portion 30 of the aperture in anvil 26 when the swaging tool is positioned as illustrated in FIG. 1.

Intermediate its ends spindle 12 is formed with an integral portion 32 having flat surfaces 34, 36 which are equidistant from the longitudinal axis of the spindle and parallel thereto. An aperture 38 extends between these two surfaces and is aligned so that its longitudinal axis intersects the longitudinal axis of the spindle and is perpendicular thereto. A cylindrical roller support shaft 40 is mounted within aperture 38 and projects from each of the surfaces 34, 36, with beveled rollers 42, 44 being respectively rotatably engaged on the ends of said shaft at the same distance from the longitudinal axis of spindle 12. Each roller comprises a shoulder portion 46 which abuts the adjacent surface 34, 36, a circumferentially extending surface 48 which is inclined at an angle of 23 relative to the longitudinal axis of shaft 40, and another circumferentially extending surface 50 which is inclined at a greater angle relative to said axis and which may be omitted in some embodiments of the invention. Adjacent each end of shaft 40 is a circumferentially extending groove (not shown) which is adapted to receive the inner edge of an annular spring clip 52, 54 which engages the end surface of the adjacent roller 42, 44 and serves to hold the latter in proper position on said shaft.

The spacing between rollers 42, 44 is such that the distance between their inner sides (i.e., the surfaces which respectively extend from the shoulder portions 46 of said rollers to the large diameter edges 56 of their beveled surfaces 48 and which are perpendicular to the longitudinal axis of shaft 40) is about 0.005 inch (preferably with a tolerance of 10.0005 inch) less than the center-to-center diameter of two annular, V-shaped grooves 58, 60 which are respectively formed on opposite sides of race 20 (said center-to-center diameter being designated D in FIG. 1 and being measured at the center of the slightly rounded bottoms of the V-shaped grooves). The walls of the grooves are inclined at an angle of 30 relative to the longitudinal axis of spindle 12, so that the included angle between the walls of each groove is 60. The grooves are concentric with respect to the peripheral wall of race 20 and are spaced only a small distance inwardly from the chamfered edges thereof, thus defining an annular, peripheral shoulder 62, 64 on each side of said race. It is important that the radius of curvature of edge 56 of each roller be in the range of about 0.010 to about 0.015 inch.

Illustrated in FIG. 2 is a second support anvil 66 which differs from anvil 26 in that it is formed with a beveled end surface 68 inclined at an angle of 67 relative to the longitudinal axis of anvil 66. Each anvil 26, 66 is provided with an air vent hole 70, 72 which extends through the lower portion of the wall thereof, and is preferably also provided with a base portion 74, 76 having an increased diameter.

Tool 10 was developed during an extensive program inch (plus or minus 0.0005 inch) less than the center-tocenter diameter of said groove. Furthermore, the thickness of the bearing race (i.e., the distance between the surfaces in which grooves 58 and 60 are formed) should be equal to, or

directed toward elminating installation defects in highnot more than 0.010 inch greater than, the thickness of the strength bearing and housing assemblies of the type illustrated housing, and the width of the chamfers on said housing (i.e., in FIGS. 1 and 2 (and also installation defects in bearing and the horizontal distance in FIG. 1 between the inner and outer housing assemblies wherein the edge of the bore in a housing edges of one of said chamfers) and the depth of each groove in is swaged, as in the assembly which is illustrated in FIGS. 3 said bearing race should be as specified in the following table: and 4 and which will be described hereinafter). In housing 24 the chamfered edges of the bore 22 thereof are inclined at an TABLE angle of 45 relative to said bore (which is the conventional arrangement), and prior to the discovery of the invention dis- I closed herein great difficulty was encountered in attempts to Beam; Race Hwsmg Chamf swage, or deform, the shoulders 62, 64 of a high-strength spherical bearing race against such chamfered bore edges 015-0030 1" X th t distortin the race and bindin the rotatable member 0020-0030 X 45 g g 0045-0050 inch 0.025-0035 inch x 45' 16 therein, galling the grooves 58, 60 which define said shoulders, or cracking the shoulders themselves. A factor which has 20 been found Critical to the design of a yp tool which in accordance with the invention the procedure for incan swage an annular shoulder on a bearing race or housing stalling a high-strength spherical bearing 18 in the bore 22 of a without causing defects of the aforedescribed type is the locahousing 24 i as follows. The groove 58 in one side of the race tion of the large diameter edges 56 of the rollers of said tool of the bearing is lubricated with a suitable lubricant, such as relative to the center of a V-shaped groove into which the rol- 25 that specified as MlL-G-Zl 164 grease. The race of thebearlers are pressed to swage said shoulder. Other critical factors ing is centered relative to the sides of the housing, as by supare the radius of curvature of said large diameter edge 56 and porting both the race and the housing on the flat end of anvil the angle of inclination of the swaging surface 48 of the rol- 26. Ram 14 is lowered to insert the lower end of spindle l2 lers. In accordance with the invention, an improved swaging within the aperture in member 16 of the bearing and within tool 10, for use in deforming a shoulder defined on one side of portion 30 of the aperture in said anvil 26, thus aligning the a race by an annular, V-shaped groove therein, is arranged as spindle in coaxial relation with the race and bringing the swagdescribed hereinbefore, namely, the swaging surfaces 48 of its ing surfaces 48 of rollers 42 and 44 against diametrically oprollers 42, 44 are inclined at an angle of 23 relative to the lonposed points on the inner edge of shoulder 62. With a first gitudinal axis of the shaft 48 on which the rollers are mounted, predetermined pressure exerted axially upon the swaging tool the radius of curvature of the large diameter edge 56 of each 10 by means of ram 14, the spindle 12 of said tool is rotated at swaging surface is within the range of about 0.010 to about least half of a revolution about its longitudinal axis. The pres- 0.0l5 inch, and the inner sides of said rollers which extend sure exerted against the spindle is then increased to a second from edges 56 are equidistant from and parallel to the longitupredetermined level as the spindle continues to rotate. To dinal axis of spindle l2 and the spacing therebetween is 0.005 minimize work-hardening of shoulder 62 the spindle should TABLE II Initial load Maximum load Bearing manufacturer Bearing part number Pounds P.s.i. Pounds 1.s.i.

Helm Universal Corp 3-246-7 450 225 1,100 350 U.S. Bearing HSP8-112 450 225 1,100 350 Transport Dynamics 55564 450 225 1,100 350 Heim Universal Corp NG-GAH 350 240 850 315 Fafnir FBUIZAZH28-1 350 240 850 315 Transport Dynamics 55565 350 240 850 315 U.S. Bearing HSP6-106 350 240 850 315 Heim Universal Corp LHSSG-4AF 225 230 500 265 Fal'nir WSBUSAZHZO-l 225 230 500 265 Transport Dynamics 55566 225 230 500 265 U.S. Bearing HSP4-105 225 230 500 265 Kahr W134-2OCRG 250 235 550 270 Transport Dynamics 55282 250 235 550 270 U.S. Bearing HU4-134 250 235 550 270 Astro AW4V ORG 250 235 550 270 Southwest. BSSR 4804 250 235 550 270 Kahr WB5-2OORG 250 235 700 290 55283 250 235 700 200 S Bea ng H U5-134 250 235 700 200 AW5V ORG 250 235 700 200 BSSR 5544 250 235 700 290 KSSBLO-32 750 300 1.500 410 55491 750 300 1,500 410 KSSB20-33 1,000 335 2,100 490 5490 1,000 335 2,100 490 MS2l230-5 250 235 700 290 LHssG-4AK 225 475 260 KSSB 30-8 350 240 800 310 Transport Dynamics 55532 350 240 800 310 Heim Universal Corp. LHSSG-6AL 250 235 550 270 AW6V CRG 350 240 800 310 KWB6-20CRO 350 240 800 310 BSSR 6341 350 240 800 310 Transport Dynamics 55284 350 240 800 310 U.S. Bearing UG-l34 350 240 800 310 Kahr KSSB22-12 1,000 335 2,100 490 Transport Dynami 55402 1,000 335 2,100 490 Heim Universal C0rp LHSSG-ISAN 250 235 600 280 LHSSG-4AE 250 235 550 270. F B S8-3 250 235 550 270 55567 250 235 550 270 161-2248 250 235 550 270 HSP4-106 250 235 550 270 not be rotated more than three revolutions while the pressure applied to it is being increased. After the pressure has reached the second level the spindle is rotated at least half of a revolution, but preferably no more than two revolutions, and then the pressure applied to the spindle is immediately relieved. It is important to keep the spindle rotating after swaging of shoulder 62 is initiated. As the foregoing steps are carried out the shoulder is displaced radially of bearing 18 so that it abuts the chamfer on the edge of the bore 22 of housing 24. However, the edges 56 of rollers 42 and 44 do not bottom in groove 58.

The housing and bearing assembly is then turned over and the race of the bearing is supported on the beveled end surface of anvil 66, which surface is inclined at the proper angle to engage the inner side of shoulder 62 after it has been swaged. Shoulder 64 of the race is thereafter swaged against the other chamfered edge of bore 22 by repeating the steps used to swage shoulder 62.

The initial and maximum pressures which are required to swage the shoulders of different bearings will depend upon such factors as the size of the bearing, the material of which its race is made, and the width of the shoulders 62, 64, thereon. For the purpose of illustration, the initial and maximum pressures which are satisfactory for use with particular spherical bearings are listed in Table II Second Embodiment The swaging tool 100 which is illustrated in FIGS. 3 and 4 is identical to the above-described tool except for the arrangement of its rollers 142, 144. In FIG. 3 reference number 126 designates a support anvil which corresponds to anvil 26 of FIG. 1, reference number 180 designates generally a bearing housing formed with a bore 182, and reference number 184 designates generally a spherical bearing the race 186 of which is different from the race of the aforedescribed bearing 18. More particularly, in the bearing and housing assembly which is illustrated in FIGS. 3 and 4 the peripheral edges of race 186 are chamfered at an angle of 45 relative to the sides of said race (which is the conventional arrangement in installations wherein the swaging shoulders are on the bearing housing instead of the bearing race), and annular shoulders 188, 190 are defined on opposite sides of housing 180 by annular, V-shaped grooves 192, 194 which are concentric to bore 182 and respectively located near the edges thereof. As in the case of grooves 58 and 60 on race 20 of FIG. 1, the bottoms of grooves 192 and 194 are slightly rounded. Each roller 142, 144 is formed with a shoulder portion 146 which abuts an adjacent flat surface 134, 136 on spindle 112, a circumferentially extending surface 148 which is inclined at an angle of 23 relative to the longitudinal axis of the roller support shaft 140, and another circumferentially extending surface 150 which is inclined at a greater angle relative to said axis and which may be omitted in some embodiments of the invention. As in the arrangement of tool 10, rollers 142, 144 are held in proper position on their support shaft by annular spring clips 152, 154 the inner edges of which are respectively engaged in grooves extending circumferentially of said shaft. The swaging surfaces 148 of rollers 142 and 144 converge toward spindle 112 whereas the swaging surfaces 48 of rollers 42 and 44 of swaging tool 10 diverge toward their supporting spindle 12. The large diameter edge 156 of each roller 142, 144 has a radius of curvature within the range of about 0.010 to about 0.015 inch (as in the case of the large diameter edges of rollers 42 and 44 of tool 10), and the outer sides of said rollers are parallel with the longitudinal axis of spindle 112 and equidistant therefrom.

If housing 180 is made of a relatively soft metal, swaging tool 100 may be used to displace the edges of bore 182 over the chamfered edges of race 186 even though no V-shaped grooves 192, 194 are formed in the sides of said housing adjacent said boreedges. However, if the housing is made of a high-strength alloy it is necessary to provide grooves 192, 194 which define shoulders 188, 190 adjacent the edges of bore 182, and it has been found preferable to make the center-tocenter diameter of each groove equal to D, plus 2D,, where D is the nominal outside diameter of race 186 (i.e., the dimension midway between the allowable minimum and maximum outside diameters of said race) and D, is the width of the chamfers on said race (i.e., the horizontal distance in FIG. 3 between the inner and outer edges of the chamfers on the race). The distance d" (see FIG. 3) between the outer sides of rollers 142 and 144 should be D, plus 2D plus 0.005 inch (plus or minus 0.0005 inch). In addition, the thickness of housing should be equal to, or not more than 0.010 inch greater than, the thickness of race 186, and the width of the chamfers on said race and the depth of each groove in said housing should be as specified in the following table:

TABLE III 0.010-0.020 inch X 45 0020-0030 inch X 45 0025-0035 inch X 45" 0.0lS-0.030 inch 0025-0040 inch 0045-0060 inch The method of using tool 100 is the same as that described in connection with tool 10 and thus it is not considered necessary to repeat the steps involved. After one shoulder 188 has been swaged against the chamfered edge of race 186, the housing and bearing assembly is turned over and said housing is supported on a second anvil 166 the upper end surface 168 of which is inclined at an angle of 67 relative to the longitudinal axis of said anvil and which is thus adapted to abut shoulder 188 after the latter has been swaged. The predescribed swaging steps are then repeated to swage shoulder 190 against the other chamfered edge of race 186.

In some bearing and housing installations only one shoulder has to be swaged in order to retain the race of the bearing within the bore of the housing, a flange being formed on the race of the bearing which fits within a recess circumscribing the edge of the bore at one end thereof or a flange being formed on the housing at one end of the bore and projecting over the periphery of the bearing. The method and tools which have been disclosed are of course applicable for swaging the single shoulder of such installations.

As various modifications of the disclosed embodiments of the invention will be obvious in view of the teachings thereof, the scope of the invention should be considered to be limited only by the terms of the claims appended hereto.

What is claimed as new and useful and desired to be secured by US. Letters Patent is:

1. A tool for securing a bearing race within a bore in a housing by swaging a shoulder defined on one of said race and said housing by an annular groove having a substantially V-shaped cross section comprising:

a spindle one end of which fits snugly within the rotatable member of said bearing;

a shaft fixedly mounted on said spindle, the longitudinal axes of said shaft and spindle intersecting at a right angle; and

a pair of beveled rollers respectively mounted on said shaft on opposite sides of said spindle, said rollers being beveled at an angle of about 23 relative to the longitudinal axis of said shaft and the radius of their large diameter edges being in the range of about 0.010 to about 0.015 inch.

2. A tool as defined in claim 1 wherein said shoulder and groove are on said race and the distance between the inner sides of said rollers is about 0.005 inch less than the center-tocenter diameter of said groove.

3. A tool as defined in claim 1 wherein said groove is on said housing and said shoulder is swaged against a 45 chamfer on said bearing race, the center-to-center diameter of said groove is equal to D plus 2D where D is the nominal outside diameter of said race and D is the width of the chamfers on said race, and the distance between the outer sides of said rollers is equal to D, plus 2D plus about 0.005 inch.

4. [n the process wherein a bearing race is secured within a bore in a housing by swaging a shoulder defined on one of said race and said housing by an annular groove having a substantially V-shaped cross section and wherein said swaging is effected by a tool comprising a spindle one end of which fits snugly within the rotatable member of said bearing, a shaft mounted on said spindle in perpendicular relation therewith, and a pair of beveled rollers respectively mounted on said shaft on opposite sides of said spindle, the steps of:

pressing said rollers against said shoulder under a first predetermined pressure and simultaneously rotating said spindle at least half of a revolution about its longitudinal axis;

increasing the pressure exerted by said rollers against said shoulder to a second predetermined pressure while continuing to rotate said spindle; and

thereafter rotating said spindle at least half of a revolution about its longitudinal axis while said rollers are pressed against said shoulder under said second pressure.

5. The process of claim 4 wherein said spindle is rotated at least three revolutions about its longitudinal axis while said rollers are pressed against said shoulder under said second pressure.

6. The process of claim 4 wherein said rollers are beveled at an angle of about 23 relative to the longitudinal axis of said shaft and the radius of their large diameter edges is in the range of about 0.010 to about 0.015 inch.

7. The process of claim 6 wherein said shoulder and groove are on said race and the distance between the inner sides of said rollers is about 0.005 inch less than the center-to-center diameter of said groove.

8. The process of claim 6 wherein said groove is on said housing and said shoulder is swaged against a 45 chamfer on said bearing race, the center-to-center diameter of said groove is equal to D plus 2D where D is the nominal outside diameter of said race and D is the width of the chamfers on said race, and the distance between the outer sides of said rollers is equal to D plus 2D plus about 0.005 inch 

1. A tool for securing a bearing race within a bore in a housing by swaging a shoulder defined on one of said race and said housing by an annular groove having a substantially V-shaped cross section comprising: a spindle one end of which fits snugly within the rotatable member of said bearing; a shaft fixedly mounted on said spindle, the longitudinal axes of said shaft and spindle intersecting at a right angle; and a pair of beveled rollers respectively mounted on said shaft on opposite sides of said spindle, said rollers being beveled at an angle of about 23* relative to the longitudinal axis of said shaft and the radius of their large diameter edges being in the range of about 0.010 to about 0.015 inch.
 2. A tool as defined in claim 1 wherein said shoulder and groove are on said race and the distance between the inner sides of said rollers is about 0.005 inch less than the center-to-center diameter of said groove.
 3. A tool as defined in claim 1 wherein said groove is on said housing and said shoulder is swaged against a 45* chamfer on said bearing race, the center-to-center diameter of said groove is equal to D1 plus 2D2 where D1 is the nominal outside diameter of said race and D2 is the width of the chamfers on said race, and the distance between the outer sides of said rollers is equal to D1 plus 2D2 plus about 0.005 inch.
 4. In the process wherein a bearing race is secured within a bore in a housing by swaging a shoulder defined on one of said race and said housing by an annular groove having a substantially V-shaped cross section and wherein said swaging is effected by a tool comprising a spindle one end of which fits snugly within the rotatable member of said bearing, a shaft mounted on said spindle in perpendicular relation therewith, and a pair of beveled rollers respectively mounted on said shaft on opposite sides of said spindle, the steps of: pressing said rollers against said shoulder under a first predetermined pressure and simultaneously rotating said spindle at least half of a revolution about its longitudinal axis; increasing the pressure exerted by said rollers against said shoulder to a second predetermined pressure while continuing to rotate said spindle; and thereafter rotating said spindle at least half of a revolution about its longitudinal axis while said rollers are pressed against said shoulder under said second pressure.
 5. The process of claim 4 wherein said spindle is rotated at least three revolutions about its longitudinal axis while said rollers are pressed against said shoulder under said second pressure.
 6. The process of claim 4 wherein said rollers are beveled at an angle of about 23* relative to the longitudinal axis of said shaft and the radius of their large diameter edges is in the range of about 0.010 to about 0.015 inch.
 7. The process of claim 6 wherein said shoulder and groove are on said race and the distance between the inner sides of said rollers is about 0.005 inch less than the center-to-center diameter of said grOove.
 8. The process of claim 6 wherein said groove is on said housing and said shoulder is swaged against a 45* chamfer on said bearing race, the center-to-center diameter of said groove is equal to D1 plus 2D2 where D1 is the nominal outside diameter of said race and D2 is the width of the chamfers on said race, and the distance between the outer sides of said rollers is equal to D1 plus 2D2 plus about 0.005 inch. 